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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi only. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is also given. The larger this ratio is, the harder the integral is to solve. In this test file, problem number [73] had the largest ratio of [1.66667000000000010]

# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 5 4 0.81 12 0.333
2 A 5 4 0.80 14 0.286
3 A 7 6 1.03 25 0.240
4 A 6 5 1.03 25 0.200
5 A 5 4 1.01 23 0.174
6 C 12 11 0.66 25 0.440
7 A 2 2 1.00 25 0.080
8 A 3 3 0.99 25 0.120
9 A 4 4 1.01 25 0.160
10 A 5 5 1.02 25 0.200
11 A 5 4 0.94 25 0.160
12 A 5 4 0.98 25 0.160
13 A 5 4 1.03 25 0.160
14 A 2 2 1.09 21 0.095
15 A 5 4 1.00 25 0.160
16 A 6 5 0.93 25 0.200
17 A 7 6 0.97 25 0.240
18 A 7 6 1.03 27 0.222
19 A 6 5 1.03 27 0.185
20 A 5 4 1.01 27 0.148
21 A 4 3 1.00 27 0.111
22 A 5 4 0.99 27 0.148
23 A 6 5 1.00 27 0.185
24 A 7 6 1.01 27 0.222
25 A 9 8 0.98 27 0.296
26 A 8 7 0.98 27 0.259
27 A 7 6 0.97 27 0.222
28 A 8 7 0.96 27 0.259
29 A 9 8 0.96 27 0.296
30 A 3 3 1.00 11 0.273
31 N/A 1 0 1.00 40 0.000
32 A 7 6 1.00 40 0.150
33 A 6 5 1.01 40 0.125
34 A 4 3 0.95 38 0.079
35 N/A 1 0 1.00 40 0.000
36 N/A 1 0 1.00 40 0.000
37 A 2 2 1.00 11 0.182
38 A 2 2 1.00 11 0.182
39 A 2 2 1.00 9 0.222
40 A 3 2 1.00 7 0.286
41 A 2 2 1.00 11 0.182
42 A 2 2 1.00 11 0.182
43 A 2 2 1.00 11 0.182
44 A 2 2 1.00 9 0.222
45 A 3 2 1.00 7 0.286
46 A 2 2 1.00 11 0.182
47 A 3 2 1.00 7 0.286
48 A 7 6 1.29 15 0.400
49 A 6 5 1.30 13 0.385
50 A 5 4 1.40 11 0.364
51 N/A 1 0 1.00 15 0.000
52 A 8 7 1.29 21 0.333
53 A 7 6 1.26 19 0.316
54 A 6 5 1.26 17 0.294
55 N/A 1 0 1.00 21 0.000
56 A 9 8 1.28 21 0.381
57 A 8 7 1.26 19 0.368
58 A 7 6 1.26 17 0.353
59 N/A 1 0 1.00 21 0.000
60 A 3 2 1.00 7 0.286
61 A 7 6 1.29 15 0.400
62 A 6 5 1.30 13 0.385
63 A 5 4 1.40 11 0.364
64 N/A 1 0 1.00 15 0.000
65 A 9 8 1.29 21 0.381
66 A 8 7 1.26 19 0.368
67 A 7 6 1.26 17 0.353
68 N/A 1 0 1.00 21 0.000
69 A 8 7 1.28 21 0.333
70 A 7 6 1.26 19 0.316
71 A 6 5 1.26 17 0.294
72 N/A 1 0 1.00 21 0.000
73 A 6 5 1.00 3 1.667
74 A 7 6 1.04 5 1.200
75 A 8 7 1.05 7 1.000
76 A 9 8 1.09 15 0.533
77 A 8 7 1.10 15 0.467
78 A 7 6 1.10 13 0.462
79 A 6 5 1.08 7 0.714
80 N/A 1 0 1.00 15 0.000
81 A 7 6 1.24 15 0.400
82 A 6 5 1.28 13 0.385
83 A 5 4 1.36 11 0.364
84 N/A 1 0 1.00 15 0.000
85 A 9 8 1.18 19 0.421
86 A 8 7 1.17 17 0.412
87 A 7 6 1.16 15 0.400
88 N/A 1 0 1.00 19 0.000
89 A 8 7 1.17 22 0.318
90 A 7 6 1.17 20 0.300
91 A 6 5 1.17 18 0.278
92 N/A 1 0 1.00 22 0.000
93 A 9 8 1.09 15 0.533
94 A 8 7 1.10 15 0.467
95 A 7 6 1.10 13 0.462
96 A 6 5 1.08 7 0.714
97 N/A 1 0 1.00 15 0.000
98 A 7 6 1.25 15 0.400
99 A 6 5 1.28 13 0.385
100 A 5 4 1.36 11 0.364
101 N/A 1 0 1.00 15 0.000
102 A 9 8 1.18 19 0.421
103 A 8 7 1.18 17 0.412
104 A 7 6 1.16 15 0.400
105 N/A 1 0 1.00 19 0.000
106 A 8 7 1.17 22 0.318
107 A 7 6 1.16 20 0.300
108 A 6 5 1.17 18 0.278
109 N/A 1 0 1.00 22 0.000
110 A 4 3 1.00 4 0.750
111 A 5 4 0.90 6 0.667
112 A 6 5 1.02 8 0.625
113 A 4 3 0.96 8 0.375
114 A 5 4 0.96 10 0.400
115 A 6 5 1.06 12 0.417
116 A 9 8 0.90 12 0.667
117 A 6 5 1.03 14 0.357
118 A 7 6 1.06 16 0.375
119 A 7 6 1.32 10 0.600
120 A 4 4 1.18 8 0.500
121 A 6 6 1.16 14 0.429
122 A 6 5 1.00 8 0.625
123 A 1 1 1.00 14 0.071
124 A 1 1 1.00 19 0.053
125 A 2 2 1.00 26 0.077
126 A 11 10 1.09 21 0.476
127 A 10 9 1.10 21 0.429
128 A 9 8 1.12 19 0.421
129 A 8 7 1.11 18 0.389
130 A 7 6 1.00 21 0.286
131 A 8 7 1.07 21 0.333
132 A 9 8 1.12 21 0.381
133 A 10 9 1.10 21 0.429
134 A 2 2 1.00 39 0.051
135 A 2 2 1.00 39 0.051
136 A 2 2 1.00 37 0.054
137 A 2 2 1.00 39 0.051
138 A 2 2 1.00 39 0.051
139 A 2 2 1.00 39 0.051
140 A 2 2 1.00 40 0.050
141 A 2 2 1.00 40 0.050
142 A 2 2 1.00 38 0.053
143 A 2 2 1.00 40 0.050
144 A 2 2 1.00 40 0.050
145 A 2 2 1.00 40 0.050
146 A 6 5 0.88 24 0.208
147 A 6 5 0.96 20 0.250
148 A 8 7 1.01 20 0.350
149 A 13 12 0.97 20 0.600
150 A 13 12 0.97 20 0.600
151 A 9 8 1.01 20 0.400
152 A 7 6 0.94 20 0.300
153 A 2 2 1.00 24 0.083

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